ABSTRACT
In this paper, a frictional viscoplastic contact problem is studied. The damage, caused by excessive stress or strain is also included and it is modelled by a parabolic differential inclusion. The variational formulation for this problem is obtained and the existence of a unique solution is proved. Then, fully discrete approximations are introduced based on the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. Error estimates are derived and, under suitable regularity assumptions, the linear convergence of the algorithm is derived. Finally, a numerical test is provided.